   Chapter 10, Problem 12PS

Chapter
Section
Textbook Problem

Arc Length A particle is moving along the path described by the parametric equations x = 1 t   and   y = sin t t for 1 ≤ t < ∞ , as shown in the figure. Find the length of this path. To determine

To calculate: The length of the path x=1t,y=sintt.

Explanation

Given:

The path is described from the following parametric equations where t starts from 1 and keeps on increasing indefinitely.

x=1ty=sintt

Formula Used:

The arc length for a parametric curve defined by the equation x(t) and y(t) where t varies between a and b is given by the equation:

A=ab(x'(t))2+(y'(t))2dt

Calculation:

For the provided parametric curve:

x(t)=1tx'(t)=1t2y(t)=sintty'(t)=tcostsintt2

This gives the arc length as:

A=

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